There are several Ideas here about using flywheels for energy storage. It is, I think, generally acknowledged that to reduce friction, the flywheel should be spun up in a vacuum, and maglev should be used to support its weight.
However, that's not all that "maglev" (in quotes for a reason!) can be
used for. Let's approach this design by first considering the original flywheel design: a fairly simple spoked wheel, with most of the mass in the wheel. Its purpose was basically to smooth out any irregularities in the rotational motion of any machine that converted reciprocating motion into rotary motion.
When people began thinking about using flywheels for energy storage (see link), calculations showed that that design was far from ideal at any practical rotation speed. A design that could store rather more energy was a sort of solid disk with significant bulges in the middle, where the axle was.
As you probably know, the problem with a high-speed flywheel is that the material from which it is constructed typically needs to have tremendous tensile strength, to hold the wheel together against the forces that appear as a result of its rotation.
This Idea is about a different way to balance those forces: maglev.
Let's construct our flywheel in the form of a simple cylinder. Let the outer curved surface of the cylinder be covered with very strong permanent magnets. A simple cutaway side view ASCII sketch, of the cylinder tipped on its side:
| body of cylinder (edge below)
N S N S N S N S N S N S (magnetic polarities)
N S N S N S N S N S N S
______________________ (wall of cylindrical container)
Since the HalfBakery does not support HTML underlining, there is a gap portrayed between the wall electromagnets and the wall; actually those electromagnets are in the wall, the same as the cylinder permanent magnets are in the cylinder. As portrayed, there is magnetic repulsion between the cylinder and the container wall. The magnets, of course, are so numerous as to be located all the way around both the exterior of the cylinder and the interior of the flywheel container body (one should think of them as continuous magnetic rings).
When oriented vertically, the weight of our massive flywheel cylinder floats on more magnets (not portrayed) --and that weight ensures that the cylinder doesn't "shift" so that the portrayed repulsion becomes attraction.
What happens when we start rotating this flywheel/cylinder at high speed? Obviously stresses will begin to appear, attempting to cause the cylinder to fly to pieces. However, because the container wall magnets are electromagnets, we can power them up and increase the magnetic repulsion between them and the cylinder. (Obviously we also want these electromagnets to be of the superconductive variety, in order to not waste energy.)
The more magnetic repulsion we can create, the faster our flywheel/cylinder can be spun, and the more energy it will store. All the force that tries to tear the cylinder apart is effectively transmitted through the magnetic fields to the body of the container, and that body can be constructed of materials that can hugely resist compressive forces, like reinforced concrete.
Because of the total weight, it would probably be unwise to put this sort of flywheel in any vehicle smaller than a ship, but to use it anywhere on land would be perfectly practical, for temporary energy storage purposes (such to hold solar power gathered during daytime for use at night).